Question

Chapter 10 Section 1 Additional Problem 1 Consider the hypothesis test Ho: M1 = H2 against H:41 <H2 with known variances j = 10 and 62 = 5. Suppose that sample sizes nj = 10 and 12 = 15 and that Ij = 14.2 and 12 = 19.7. Use a = 0.05. (a) Test the hypothesis and find the P-value. (b) What is the power of the test in part (a) if u1 is 4 units less than 2? (c) Assuming equal sample sizes, what sample size should be used to obtain B = 0.05 if H1 is 4 units less than Hl2? Assume that a = 0.05. (a) The null hypothesis rejected. The P-value is Round your answer to four decimal places (e.g. 98.7654). (b) The power is Round your answer to two decimal places (e.g. 98.76). (c) ni = n2 = Round your answer up to the nearest integer.

Answer 1

a) The null hypothesis is not rejected. The P=value is 0.0537.

b) The power is 0.32

c) n₁=n₂=85

Here is the solution:

al The pooled variance is given by. 2 + 25 s 1.667 h₂ 10 -1.61 The test statistic is given by. X.- X2 14.2-19.7 22 var 67 Thus the P-value P(Z<-1.6i) = 0.05 37 This, at level a=0.05, we fail to reject the hell hypothesis b) Under Ho and at the level a=0.05, we reject the hull hypothesis if 2<-1.645 thus the power is given by. < 1.645) as under Hal 1-61 X-32t4 ~ MOD = P(8 - x2 +4 El.bustu = P(Z <-1645+ 4 then ) = (0.32.18 (c) If we equal sample size then the Poded variance is P(x - 72 assume 125 n 62, Thus, Power of the test at a=0.05 is <-4.645) - PC X-Fath 57.645 + 123 It we need B:o.05 ) Power =0.95 thun, we need lib45+ 45n -1-645 VI2s n = 2x1.6455125 = 9.196 =) = 84.56 nearest integer is 4 nr 85